Solving DLP with Auxiliary Input over an Elliptic Curve Used in TinyTate Library

Sakemi, Yumi; Izu, Tetsuya; Takenaka, Masahiko; Yasuda, Masaya

doi:10.1007/978-3-642-21040-2_8

Cited by 3 publications

(2 citation statements)

References 14 publications

(27 reference statements)

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“…[17] 60 3 hours ρ-method Izu, Takenaka, Yasuda [15,16] 83 14 hours BSGS method Sakemi et al [21] 128 131 hours BSGS method Sakemi et al [22] 128 136 hours ρ-method This paper 160 1314 days ρ-method…”

Section: Introductionmentioning

confidence: 98%

Solving a Discrete Logarithm Problem with Auxiliary Input on a 160-Bit Elliptic Curve

Sakemi

Hanaoka

Izu

et al. 2012

Public Key Cryptography – PKC 2012

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Abstract.A discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α from G, αG, α d G in an additive cyclic group generated by an element G of prime order r, and a positive integer d satisfying d|(r − 1). The infeasibility of this problem assures the security of some cryptographic schemes. In 2006, Cheon proposed a novel algorithm for solving DLPwAI (Cheon's algorithm). This paper reports our experimental results of Cheon's algorithm by implementing it with some speeding-up techniques. In fact, we have succeeded to solve DLPwAI on a pairing-friendly elliptic curve of 160-bit order in 1314 core days. Implications of our experiments on cryptographic schemes are also discussed.

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Section: Introductionmentioning

confidence: 98%

Solving a Discrete Logarithm Problem with Auxiliary Input on a 160-Bit Elliptic Curve

Sakemi

Hanaoka

Izu

et al. 2012

Public Key Cryptography – PKC 2012

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“…Jao, et al implemented Cheon's algorithm with the kangaroo method 14) . Moreover, Sakemi, et al implemented Cheon's algorithm with both methods 19) . Note that their works were implemented on elliptic curves over a prime field.…”

Section: Introductionmentioning

confidence: 99%

Experimental Analysis of Cheon's Algorithm against Pairing-friendly Curves

Izu

Takenaka

Yasuda

2011

Journal of Information Processing

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Let G be an additive group generated by an element G of prime order r. The discrete logarithm problem with auxiliary input (DLPwAI) is a problem to find α on inputs G, αG, α d G ∈ G for a positive integer d dividing r − 1. The infeasibility of DLPwAI ensures the security of some pairing-based cryptographic schemes. In 2006, Cheon proposed an algorithm for solving DLPwAI which works better than conventional algorithms. In this paper, we report our experimental results of Cheon's algorithm on a pairing-friendly elliptic curve defined over GF(3 127). Moreover, based on our experimental results, we estimate the required cost of Cheon's algorithm to solve DLPwAI on some pairing-friendly elliptic curves over a finite field of characteristic 3. Our estimation implies that DLPwAI on a part of pairing-friendly curves can be solved at reasonable cost when the optimal parameter d is chosen.

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